Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do μ not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. n a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? OA. Ho: H₁ H2 H₁ H₁ H₂ OC. Ho: H₁ H₂ H₁ H₁ H₂ O B. Ho: H=H2 H₁ H₁ H₂ OD. Ho: H1 H₁: H₁ H₂ H₂ X S Diet H1 33 0.79376 lb 0.00435 lb Regular H₂ 33 0.80961 lb 0.00742 lb
Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do μ not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. n a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. What are the null and alternative hypotheses? OA. Ho: H₁ H2 H₁ H₁ H₂ OC. Ho: H₁ H₂ H₁ H₁ H₂ O B. Ho: H=H2 H₁ H₁ H₂ OD. Ho: H1 H₁: H₁ H₂ H₂ X S Diet H1 33 0.79376 lb 0.00435 lb Regular H₂ 33 0.80961 lb 0.00742 lb
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Chapter1: Starting With Matlab
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Transcribed Image Text:**Educational Content: Statistical Hypothesis Testing**
**Data on Soda Can Weights:**
The table below summarizes data on the weights (in pounds) of the contents of cans of diet soda versus cans of regular soda. Assume that the two samples are independent random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. A 0.05 significance level is used for the hypothesis test.
| | Diet (μ₁) | Regular (μ₂) |
|----------------|-----------|--------------|
| Sample size (n)| 33 | 33 |
| Mean (x̄) | 0.79376 lb| 0.80961 lb |
| Standard Deviation (s) | 0.00435 lb | 0.00742 lb |
**Hypothesis Test (Part a):**
**Objective:**
Test the claim that the mean weight of the contents of diet soda cans is less than the mean weight of the contents of regular soda cans.
**Hypotheses:**
- **Null Hypothesis (H₀):** μ₁ = μ₂
- **Alternative Hypothesis (H₁):** μ₁ < μ₂
**Options for Null and Alternative Hypotheses (Choose the correct one):**
- A.
- H₀: μ₁ = μ₂
- H₁: μ₁ > μ₂
- B.
- H₀: μ₁ = μ₂
- H₁: μ₁ ≠ μ₂
- C.
- H₀: μ₁ ≠ μ₂
- H₁: μ₁ < μ₂
- **D.**
- H₀: μ₁ = μ₂
- H₁: μ₁ < μ₂
**Conclusion:**
Select option D, as it correctly represents the null and alternative hypotheses for testing if the mean weight of diet soda is less than that of regular soda.
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